Question1) Determine if the ordered pair $(3,4)$ is a solution to the equation $6 x-4 y=6$.
Find a point that does belong to this line. 2) Find the equation of the line that passes through the point $(6,4)$ and has a slope of 2.5. 3) Find the slopes and $y$-intercepts for each of the following lines: (a) $2 x+5 y=23$ (b) $2 x-3 y-8=0$ 4) Find the slopes and $y$-intercepts for each of the line that passes through the following two points: $$P(0.6,-1.3) \text { and } Q(2.3,-2.4)$$

Studdy Solution
To find the slope of the line through points $P(0.6, -1.3)$ and $Q(2.3, -2.4)$:
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2.4 + 1.3}{2.3 - 0.6} = \frac{-1.1}{1.7} \approx -0.647$$
Using point-slope form with point $P(0.6, -1.3)$:
$$y + 1.3 = -0.647(x - 0.6)$$ $$y = -0.647x + 0.3882 - 1.3$$ $$y = -0.647x - 0.9118$$
Slope $m \approx -0.647$, $y$-intercept $b \approx -0.9118$.